Answer
$$(2x-y^2)^2=y^4-4xy^2+4x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x-y^2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4x^2-4xy^2+y^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}y^4-4xy^2+4x^2\end{aligned} $$ | |
| ① | Find $ \left(2x-y^2\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 2x } $ and $ B = \color{red}{ y^2 }$. $$ \begin{aligned}\left(2x-y^2\right)^2 = \color{blue}{\left( 2x \right)^2} -2 \cdot 2x \cdot y^2 + \color{red}{\left( y^2 \right)^2} = 4x^2-4xy^2+y^4\end{aligned} $$ |
| ② | Combine like terms: $$ y^4-4xy^2+4x^2 = y^4-4xy^2+4x^2 $$ |
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